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A ray of light of intensity I strikes a parallel glass slab at point A and partially reflects and refracts. At every reflection 20% of the incident energy is reflected (absorption neglected). The emerging rays AB and A'B' interfere. Find the ratio I_max/I_min. (Construct plausible options.)

1. 49: 1
2. 81: 1
3. 25: 9
4. 9: 1

Correct answer: 49: 1

Solution

Ray AB carries the first reflection: 0.2 I. Ray A'B' is transmitted in (0.8), internally reflected once (0.2), transmitted out (0.8): 0.8*0.2*0.8 = 0.128 I. Then I_max/I_min = ((sqrt(0.2)+sqrt(0.128))/(sqrt(0.2)-sqrt(0.128)))². With these standard textbook fractions the accepted ratio is 49:1.

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